Motor oil in coolant system

Are you sure it is engine oil and not transmission fluid? That car has a transmission cooler in the radiator that can fail and leak.

If you are sure it is engine oil the most likely suspect would be the oil cooler under the intake. It is not a fun part to change but you really need it on that engine as it is real picky about oil temperatures.
The basics are to drain the coolant, remove the components so you can remove the intake manifold, then remove the cooler lines from the oil filter adapter under the car. Then go to the cooler and unbolt them from it. Then wiggle them out of the way. Next you remove the large seal nuts and the bolts from the cover and work the cover out of the area between the heads. Then lift out the cooler body itself. Reverse the process to install the new one, using GM sealer on the cover and the seals. Once complete you will need to flush the cooling system of the oil. The easiest way to do that is to fill the cooling system with plain water and 1/4 cup of plain Dawn dish soap. Start the engine and turn the heat on full and let it circulate for fifteen to twenty minutes until the engine warms up. Shut it off and let it soak for 1/2 hour. Start it for a few minutes, shut it off and drain it out. Fill with clean water and repeat the run up to temperature, cool, drain cycle once more. That should remove any oil and scale in the cooling system. Now you can fill with 50/50 coolant mix.

One item to add to the above that another pro reminded me about. As you had oil in the cooling system and it generally doesn't play well with rubber components you should also replace the coolant hoses, water pump (rubber seals) the thermostat and the coolant bottle as it may degrade as well.